RD Sharma Solutions for Class 7 Maths Chapter 3 Decimals

Mathematics is an essential part of our daily lives, and understanding the concept of decimals is crucial for students. In Class 7, Chapter 3 of RD Sharma, we dive into the fascinating world of decimals, a topic that plays a vital role in improving your numerical skills. Whether it's measuring, comparing quantities, or dealing with financial calculations, decimals are used everywhere. This chapter aims to introduce you to the basics of decimal numbers and guide you through operations like addition, subtraction, multiplication, and division involving decimals.

In this chapter, you will learn how to convert fractions to decimals, understand the importance of decimal places, and perform decimal addition and subtraction. You will also explore multiplication and division of decimals, focusing on aligning decimal points and ensuring accurate results. As you progress, you will develop the ability to handle more complex decimal problems, making you proficient in using decimals in real-world applications.

The RD Sharma Solutions for Class 7 Maths Chapter 3 Decimals are designed to help students grasp these concepts step by step. These solutions offer clear explanations, detailed stepwise methods, and tips that will make learning decimals both easy and fun. Each exercise has been crafted to enhance your understanding and improve your problem-solving abilities. The practice questions are designed to strengthen your foundation and prepare you for higher-level topics.

By mastering the skills in this chapter, you’ll gain confidence in solving decimal-related problems and apply them to everyday situations like handling money, measurements, and even scientific calculations. So, let's dive into Chapter 3 and take the first step toward mastering decimals!

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RD Sharma Class 7 Chapter 3 PDF includes detailed solutions, examples, and extra questions to help you master real numbers and other topics. Click here to download the RD Sharma Class 7 Chapter 3 PDF.

Access Answers to RD Sharma Solutions for Class 7 Maths Chapter 3 Decimals

In this chapter, students will learn about decimals and how to perform basic operations with them. The solutions provided here are detailed and easy to follow, helping students understand each concept thoroughly.

Q1. Convert the following into decimals:

1. (8/100)
2. 20 + (9/10) + (4/100)
3. 23 + (2/10) + (6/1000)

Solution:

(i) (8/100)

To convert 8/100 into a decimal, move the decimal point two places from right to left. Therefore, 8/100 = 0.08.

(ii) 20 + (9/10) + (4/100)

Convert (9/10) and (4/100) to decimals:

- (9/10) = 0.9

- (4/100) = 0.04

Therefore, 20 + 0.9 + 0.04 = 20.94.

(iii) 23 + (2/10) + (6/1000)

Convert (2/10) and (6/1000) to decimals:

- (2/10) = 0.2

- (6/1000) = 0.006

Therefore, 23 + 0.2 + 0.006 = 23.206.

Q2. Convert the following decimals to fractions:

1. 0.04
2. 2.34
3. 0.342
4. 17.38

Solution:

(i) 0.04

To convert 0.04 into a fraction, write it as 0.04/1. Then multiply both numerator and denominator by 100:

(0.04/1) = 4/100 = 1/25.

(ii) 2.34

To convert 2.34 into a fraction, write it as 2.34/1. Then multiply both numerator and denominator by 100:

(2.34/1) = 234/100 = 117/50.

(iii) 0.342

To convert 0.342 into a fraction, write it as 0.342/1. Then multiply both numerator and denominator by 1000:

(0.342/1) = 342/1000 = 171/500.

(iv) 17.38

To convert 17.38 into a fraction, write it as 17.38/1. Then multiply both numerator and denominator by 100:

(17.38/1) = 1738/100 = 869/50.

Q3. Convert the following fractions into decimals:

1. 23/10
2. 25 + (1/8)
3. 1372/35
4. 15 + (1/25)

Solution:

(i) 23/10

To convert 23/10 into a decimal, divide 23 by 10. Therefore, 23/10 = 2.3.

(ii) 25 + (1/8)

Convert (1/8) into a decimal by multiplying both the numerator and denominator by 125 to get 1000 as the denominator:

(1/8) = 0.125

Therefore, 25 + 0.125 = 25.125.

(iii) 1372/35

Divide 1372 by 35. The result is 39.2.

(iv) 15 + (1/25)

Convert (1/25) into a decimal by multiplying both the numerator and denominator by 4 to get 100 as the denominator:

(1/25) = 0.04

Therefore, 15 + 0.04 = 15.04.

Q4. Find the product:

1. 4.74 × 10
2. 0.45 × 10
3. 0.0215 × 10
4. 0.0054 × 10

Solution:

(i) 4.74 × 10

Multiply 4.74 by 10. Shift the decimal point one place to the right.

4.74 × 10 = 47.4.

(ii) 0.45 × 10

Multiply 0.45 by 10. Shift the decimal point one place to the right.

0.45 × 10 = 4.5.

(iii) 0.0215 × 10

Multiply 0.0215 by 10. Shift the decimal point one place to the right.

0.0215 × 10 = 0.215.

(iv) 0.0054 × 10

Multiply 0.0054 by 10. Shift the decimal point one place to the right.

0.0054 × 10 = 0.054.

Q5. Find the product:

1. 35.853 × 100
2. 42.5 × 100
3. 12.075 × 100
4. 100 × 0.005

Solution:

(i) 35.853 × 100

Multiply 35.853 by 100. Shift the decimal point two places to the right.

35.853 × 100 = 3585.3.

(ii) 42.5 × 100

Multiply 42.5 by 100. Shift the decimal point two places to the right.

42.5 × 100 = 4250.

(iii) 12.075 × 100

Multiply 12.075 by 100. Shift the decimal point two places to the right.

12.075 × 100 = 1207.50.

(iv) 100 × 0.005

Multiply 100 by 0.005. Shift the decimal point two places to the right.

100 × 0.005 = 0.5.